Elliptic flow in transport theory and hydrodynamics

We present a new direct simulation Monte-Carlo method for solving the relativistic Boltzmann equation. We solve numerically the 2-dimensional Boltzmann equation using this new algorithm. We find that elliptic flow from this transport calculation smoothly converges towards the value from ideal hydrodynamics as the number of collisions per particle increases, as expected on general theoretical grounds, but in contrast with previous transport calculations.Comment: 5 pages, 3 figures, revise

On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state

We show that a pair of conjectures raised in [11] concerning the construction of normal solutions to the relativistic Boltzmann equation are valid. This ensures that the results in [11] hold for any range of positive temperatures and that the relativistic Euler system under the kinetic equation of state is hyperbolic and the speed of sound cannot overcome $c/\sqrt{3}$.Comment: 6 pages. Abridged version; full version to appear in Commun. Pure Appl. Ana

Linking the hydrodynamic and kinetic description of a dissipative relativistic conformal theory

We use the entropy production variational method to associate a one particle distribution function to the assumed known energy-momentum and entropy currents describing a relativistic conformal fluid. Assuming a simple form for the collision operator we find this one particle distribution function explicitly, and show that this method of linking the hydro and kinetic description is a non trivial generalization of Grad's ansatz. The resulting constitutive relations are the same as in the conformal dissipative type theories discussed in J. Peralta-Ramos and E. Calzetta, Phys. Rev. D {\bfseries 80}, 126002 (2009). Our results may prove useful in the description of freeze-out in ultrarelativistic heavy-ion collisions.Comment: v2: 23 pages, no figures, accepted in Phys. Rev.

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients carry information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion.Comment: 27 page

The enigmatic nature of the circumstellar envelope and bow shock surrounding Betelgeuse as revealed by Herschel. I. Evidence of clumps, multiple arcs, and a linear bar-like structure

Context. The interaction between stellar winds and the interstellar medium (ISM) can create complex bow shocks. The photometers on board the Herschel Space Observatory are ideally suited to studying the morphologies of these bow shocks. Aims. We aim to study the circumstellar environment and wind-ISM interaction of the nearest red supergiant, Betelgeuse. Methods. Herschel PACS images at 70, 100, and 160 micron and SPIRE images at 250, 350, and 500 micron were obtained by scanning the region around Betelgeuse. These data were complemented with ultraviolet GALEX data, near-infrared WISE data, and radio 21 cm GALFA-HI data. The observational properties of the bow shock structure were deduced from the data and compared with hydrodynamical simulations. Results. The infrared Herschel images of the environment around Betelgeuse are spectacular, showing the occurrence of multiple arcs at 6-7 arcmin from the central target and the presence of a linear bar at 9 arcmin. Remarkably, no large-scale instabilities are seen in the outer arcs and linear bar. The dust temperature in the outer arcs varies between 40 and 140 K, with the linear bar having the same colour temperature as the arcs. The inner envelope shows clear evidence of a non-homogeneous clumpy structure (beyond 15 arcsec), probably related to the giant convection cells of the outer atmosphere. The non-homogeneous distribution of the material even persists until the collision with the ISM. A strong variation in brightness of the inner clumps at a radius of 2 arcmin suggests a drastic change in mean gas and dust density some 32 000 yr ago. Using hydrodynamical simulations, we try to explain the observed morphology of the bow shock around Betelgeuse. Conclusions: [abbreviated]Comment: 26 page

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

Genetic variability in a population of Letelle sheep in South Africa

The purpose of the study was to gain insight into the genetic variability of the Letelle sheep breed, a breed that has been managed as a closed population for 90 years, with no new genetic material being permitted into the breed. The Letelle is a South African developed dual-purpose sheep breed and is classified as a Merino type with a Spanish Merino origin. The breed exhibits good fine wool characteristics and yields high-quality mutton. Line-breeding, family-breeding, and inbreeding are applied, and multiple sire matings are practised to prevent a sire from having a large influence on the national flock. Ear samples were collected from 10 animals each from 10 commercial and 11 seed-stock flocks and genotyped using 17 microsatellite markers. Unbiased heterozygosity ranged from 0.58 to 0.68 and the observed heterozygosity from 0.52 to 0.65. The estimated effective population size (Ne) was 228.2 - 321.9. Results from analysis of molecular variance (AMOVA), a Bayesian assignment test, and a neighbour-joining (NJ) tree suggested that no genetic sub-structure existed within this population and that the seed-stock and commercial flocks could be regarded as one genetic population. The average within flock (FIS) and within breed (FIT) inbreeding coefficients were 10.1% and 14.5%, respectively. Despite the level of inbreeding, levels of genetic diversity were moderate and potentially provide opportunities for future selection and adaptation. Further testing could identify flocks in which conservation management is required as well as those with high genetic variability, which would provide the best reservoir for selection to adapt to future climatic challenges.Keywords: genetic distance, inbreeding, microsatellite markers, population structur

Causal Relativistic Fluid Dynamics

We derive causal relativistic fluid dynamical equations from the relaxation model of kinetic theory as in a procedure previously applied in the case of non-relativistic rarefied gases. By treating space and time on an equal footing and avoiding the iterative steps of the conventional Chapman-Enskog --- CE---method, we are able to derive causal equations in the first order of the expansion in terms of the mean flight time of the particles. This is in contrast to what is found using the CE approach. We illustrate the general results with the example of a gas of identical ultrarelativistic particles such as photons under the assumptions of homogeneity and isotropy. When we couple the fluid dynamical equations to Einstein's equation we find, in addition to the geometry-driven expanding solution of the FRW model, a second, matter-driven nonequilibrium solution to the equations. In only the second solution, entropy is produced at a significant rate.Comment: 23 pages (CQG, in press

Macroscopic Equations of Motion for Two Phase Flow in Porous Media

The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore a more general system of macroscopic equations is derived here which incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach which exhibit a complex dependence on the state variables. A capillary pressure function can be identified in equilibrium which shows the qualitative saturation dependence known from experiment. In addition the new equations allow to describe the spatiotemporal changes of residual saturations during immiscible displacement.Comment: 15 pages, Phys. Rev. E (1998), in prin